H. Henry Cao

Hanzhong Cao, Wenbo Yan, Ying Tan

Many methods aim to enhance time series forecasting by decomposing the series through intricate model structures and prior knowledge, yet they are inevitably limited by computational complexity and the robustness of the assumptions. Our research uncovers that in the complex domain and higher-order hypercomplex spaces, the characteristic frequencies of time series naturally decrease. Leveraging this insight, we propose Numerion, a time series forecasting model based on multiple hypercomplex spaces. Specifically, grounded in theoretical support, we generalize linear layers and activation functions to hypercomplex spaces of arbitrary power-of-two dimensions and introduce a novel Real-Hypercomplex-Real Domain Multi-Layer Perceptron (RHR-MLP) architecture. Numerion utilizes multiple RHR-MLPs to map time series into hypercomplex spaces of varying dimensions, naturally decomposing and independently modeling the series, and adaptively fuses the latent patterns exhibited in different spaces through a dynamic fusion mechanism. Experiments validate the model`s performance, achieving state-of-the-art results on multiple public datasets. Visualizations and quantitative analyses comprehensively demonstrate the ability of multi-dimensional RHR-MLPs to naturally decompose time series and reveal the tendency of higher dimensional hypercomplex spaces to capture lower frequency features.

Wenbo Yan, Hanzhong Cao, Ying Tan

Long sequence prediction is a key challenge in time series forecasting. While Mamba-based models have shown strong performance due to their sequence selection capabilities, they still struggle with insufficient focus on critical time steps and incomplete noise suppression, caused by limited selective abilities. To address this, we introduce Repetitive Contrastive Learning (RCL), a token-level contrastive pretraining framework aimed at enhancing Mamba's selective capabilities. RCL pretrains a single Mamba block to strengthen its selective abilities and then transfers these pretrained parameters to initialize Mamba blocks in various backbone models, improving their temporal prediction performance. RCL uses sequence augmentation with Gaussian noise and applies inter-sequence and intra-sequence contrastive learning to help the Mamba module prioritize information-rich time steps while ignoring noisy ones. Extensive experiments show that RCL consistently boosts the performance of backbone models, surpassing existing methods and achieving state-of-the-art results. Additionally, we propose two metrics to quantify Mamba's selective capabilities, providing theoretical, qualitative, and quantitative evidence for the improvements brought by RCL.